III.
Prof. W. P. Allis
Prof. S. C. Brown
Prof. C. W. Garland
SOLID STATE PHYSICS
Prof. G. G. Harvey
Dr. W. M. Whitney
G. Ascarelli
R. Dalven
K. R. Dawber
T. Higier
R. G. Newburgh
RESEARCH OBJECTIVES
1.
Soft X-ray Spectroscopy
The soft X-ray spectroscopy program has as its objective the experimental study of
the structure of the conduction band of electrons in a series of metals, particularly the
alkalis, alkaline earths, and some of the transition metals.
The filled portion of such
a band can be studied by observing the emission spectrum produced by transitions from
this band to the nearest sharp levels below this band. In most metals this corresponds
to an energy in the range of 15-250 ev (wavelengths in the range 50-900A), so that the
technique of extreme ultraviolet vacuum spectroscopy is applied. The energy width of
these bands usually lies in the range of 2-10 ev. Present effort is directed to the
measurement of the copper and nickel bands in a series of copper-nickel alloys of
various compositions. A more detailed description of the procedures will be found in
the Quarterly Progress Report of January 15, 1954, page 9.
G. G. Harvey
2.
Microwave Study of Semiconductors
One of the general aims of the research on microwave study of semiconductors is to
apply the methods and general point of view of the microwave gaseous discharge work to
those problems involving semiconductors wherever it seems profitable.
S. C.
3.
Brown
Elastic Constants of Single Crystals
The development of high-speed computers and the accuracy of experimentally
obtained low-temperature specific heats have led to a revival of interest in the theory
of lattice dynamics. The vibrational frequency spectrum and the bulk thermodynamic
properties of a crystalline material can be computed by a Born-von Karman calculation
based on interatomic force constants derived from the adiabatic elastic constants of a
single crystal. Since the specific heat at low temperatures is most sensitive to the
parameters of the lattice model employed, calculations that use the elastic constants
at liquid-helium temperatures are of the greatest interest.
The adiabatic elastic constants of a crystalline substance can be calculated from
the velocities of propagation of ultrasonic waves along various crystallographic axes.
Pulsed-circuit techniques provide a convenient method for measuring these velocities.
Measurements of elastic constants for hexagonal close-packed metals and alkali halides
are in progress. Data on magnesium, an almost ideally packed metal, are complete,
as reported in the Quarterly Progress Reports for 1956. Work is almost complete on
zinc, which is highly anisotropic, and has been started on sodium iodide.
C.
4.
W. Garland
Liquid Helium Research
Two experiments are under way in the low temperature laboratory. We hope to
round out our previous measurements of the attenuation of sound in liquid helium below
(III.
SOLID STATE PHYSICS)
10 K at 12 mc, as a function of pressure, by acquiring data at 2 mc and 6 mec.
A second
project is concerned with measuring the velocity of pulsed sinusoidal waves of second
sound in the temperature range from 1 0 K, where there is very little dispersion, to
approximately 0. 3 K, where the dispersion is so great that second sound can no longer
exist as a wave motion.
The results of both of these experiments should help clarify the nature of the elementary relaxation processes that lead to the establishment of thermal equilibrium in
liquid helium at these temperatures, and possibly explain the behavior of other properties of the liquid.
W. M. Whitney
A.
RECOMBINATION OF ELECTRONS AND DONORS IN GERMANIUM
1.
Recombination
In studying the direct recombination of electrons with donors in germanium we
are using a sample of germanium which is mounted in a microwave cavity in such a
way that a voltage pulse can be applied to it.
portion of the donors are not ionized.
When the sample is at 4. Z2 K, a large
When we apply a dc (or microwave) field of
sufficient intensity, we raise the temperature of the electrons so that they ionize the
This is our breakdown picture.
remaining donors by impact.
We are studying the manner in which the number of electrons returns to the number
that corresponds to equilibrium in the absence of a field
We write
dn
dt
- an(n + Na)
where Na is the number of acceptors in our sample, which is,
however,
of type n,
the number of ionized donors is (n + Na); a is a proportionality constant = cryv,
r is the cross section for recombination,
If we impose as initial conditions n = Nd - N
N
n
N
For n
<N
d
d
-N
a
00
aN t
-n
e
-1
00
- N a , the formula becomes
N
n-n
a
Nd - n
Nd
d
where
and v is the velocity of the electrons.
solve Ricatti's equation:
n-n
and
a
aN t
a
Developing
denominator
the
in series, we obtain
Developing the denominator in series, we obtain
at t
0, and n = n
at t = o, we can
(III.
SOLID STATE PHYSICS)
N
n-n
00
=
N
Nd
d
for Nd <<N
a
1
at
Nd
a
(1 + aNt) - 1
.
The unloaded Q of a cavity is inversely proportional to the conductivity, and hence
to n, and thus we can write
Qoo
1 -
Q
We
were
1
an t
justified
in
disregarding
diffusion
because
during
the time
involved,
t z 0. 1 j sec, there is no possibility of its having an appreciable effect.
/Q) - 1 is plotted as a function of t for two different samples.
In Fig. III-1 (Q
exponent of t is approximately -1 (within 10 per cent).
The
We disregarded the points in
the graph of sample 3 that correspond to t > 0. 2 4sec, because they seem to be related
to a phenomenon which we do not yet understand.
We believe that even by using a pulsed probing field whose duration is 0. 2
p.sec and
whose incident power is approximately 10 jiwatts, we have produced a partial breakdown which is evidenced by the low Q of our cavity.
From the measurement of Q in
8
-3
the absence of a voltage pulse, we can evaluate n , which is approximately 10 cm
and
hence
9
the
y
10
o
2.
Breakdown
corresponding
cross
section
for
recombination
in
sample
3 is
cm .
We also measured breakdown fields in sample 3 by a method similar to that used
by Madan, Gordon,
Buchsbaum, and Brown (1).
for breakdown as a function of the electric field.
We observed the necessary time
The result is shown in Fig. 111-2.
By observing recombination as a function of the duration of the breakdown pulse,
for an applied field of approximately 60 v/cm, we found that there was no heating effect
in the sample or in the contacts.
Breakdown was detected by looking at a microwave
signal that was on continuously.
The beginning of breakdown corresponded to a sudden
change of the reflection coefficient of the cavity.
When the delay between the application of the breakdown field and the breakdown
itself is approximately T = 2
asymptotic value.
If we assume that T z 2 tsec is the time necessary for n
to ionize Nd - Na z Nd donors,
T =
n
1
vo
Co
sec, we find that the field has practically reached its
or
c =
1
Tnv
we can write
electrons
s t
o I
RUN
d
O 2'
A
RUN
r
3
S
Ist RUN
0
2d RUN
S3rdRUN
d RUN
h
+
4" RUN
C
A
t(
Fig. III- 1.
I
10'
10'
SEC)
Il
t(r SEC)
Decay of electron density as a function of time. (a) Sample 1,
pulse duration 0. 2 .sec. (b) Sample 3, pulse duration 2 4sec.
I
I
17
Fig. 111-2.
18
20
st
RUN
n
2 d RUN
30
FIELD(V/CM)
Beginning of breakdown as a function of applied field.
(III.
SOLID STATE PHYSICS)
Taking v = 5 x 106 cm/sec as corresponding to a temperature of approximately 100 K
-9
2
8
-3
and
and m = 0. 22 m
n
= 10 cm
, we obtain
= 10
cm , which is in agreement with
the data from recombination.
G. Ascarelli
References
1.
M. P. Madan, E. I. Gordon, S. J. Buchsbaum, S. C. Brown, Determination of
the coefficient of diffusion and frequency of ionization in microwave discharges,
Phys. Rev. 106, 839 (1957).